Glicko Rating Changes

The next installment in the series of Starline’s Painstaking OGS Tables!

After a lot of research, and a lot of math, I made this table to find out how your rank will change! Bear in mind that these are AVERAGES. Do not come at me if they are slightly off.

The left column is your opponent’s rank relative to yours, so if you were a 1550, and played a 1580, you’d refer to the 30 in the left column. You guys can fill in the gaps I left here :slight_smile:

Rating Difference Win Rating Change Loss Rating Change
-300 +8 -40
-270 +9 -38
-240 +10 -37
-210 +11 -35
-180 +13 -33
-150 +15 -32
-120 +16 -30
-90 +18 -28
-60 +20 -26
-30 +22 -24
0 +24 -22
30 +26 -20
60 +28 -18
90 +30 -16
120 +32 -14
150 +34 -13
180 +35 -11
210 +37 -10
240 +39 -8
270 +40 -7
300 +41 -6

If you’re wondering how these translate to kyu ranks, never fear!
Here’s yet another table!

Rank Rating
25k 997
24k 1030
23k 1063
22k 1098
21k 1134
20k 1171
19k 1209
18k 1248
17k 1289
16k 1330
15k 1374
14k 1418
13k 1464
12k 1512
11k 1561
10k 1612
9k 1664
8k 1719
7k 1774
6k 1832
5k 1892
4k 1953
3k 2017
2k 2082
1k 2150
1d 2220
2d 2292
3d 2367
4d 2444
5d 2523
6d 2605
7d 2690
8d 2777
9d 2868

Source

Edits to avoid people attacking me:
This is once you have established a stable rank by playing 15 ranked games.
The 15-game window this system works on leads to some quirks, like if a game you won against a stronger opponent just leaves that window, and is replaced by a win against a weaker opponent, your rank will go down, even if you won, and vice versa for a loss against a weaker opponent.

9 Likes

Yes, yes, I know, stuff about the 15 game window, but NO ONE CARES! I just put in a bunch of placeholder games, where the opponents were all equal strength, and the outcome was a tie.

1 Like

It is 1 AM here.
Should I…

  • Get more sleep
  • Keep making charts
  • Why should I care?

0 voters

1 Like

I can ASSURE you, MANY people care… we get enough people asking “why did my rank drop after a win” that we included it in our FAQ

4 Likes

Sorry if I am just clueless or not understanding the chart, but how much would I move down if I lost to an opponent 900 rating differences above me? That should be my new strategy now :smiley: playing the people I will barely move down against. All I gotta do is catch them in a tournament or ladder challenge them.

3 Likes

The ranking win change looks linear enough? I guess that it is linear, because it is increasing by one-two-one-two

The ranking loss change is probably going to be close to zero, so yeah.
To the extremes, let’s say a 400 Glicko point person https://avavt.github.io/gotstats/#/user/636788
Beat a 3150 Glicko point person (any of the 9 dans) https://online-go.com/player/624668/ (Note: he got affected by the correspondence disconnection bug - look at his rank before that), The 400 point person would (by a linear extension of the Win Rating Change - it might not be linear but it seems that way) gain 200 Glicko points, and the 3150 point person would lose 200, but they would still be a 9d! :stuck_out_tongue: (Man pros are good)

3 Likes

It is not linear! The 3150 person would lose 53! The 400 would only gain 55!

2 Likes

It should be antisymmetric. The rating formula is antisymmetric.

The default rank of an unranked player is 1150. I don’t remember the exact averages, but I found the average rank is significantly higher than that. Assuming 60% of games are ranked, I found a (small) “compensation number” to add, so everything aligns.

1 Like

Okay, maybe the math is not perfectly linear, but it has to be at least close to linear, right? I mean, it follows a +1, +2 pattern, right?

1 Like

It is a sigmoid function.
image

3 Likes

looks up sigmoid function
What is the upper limit? (I know that sigmoid functions map numbers on the number line to a number from 0 to 1 - it is a curve (Side note: In a perfect world, a virus’s ahem COVID-19 ahem total cases would map a sigmoid function, with 0 being the bottom (or 1? It is a virus after all), and the total case number at the end would be the upper bound)). Based on my understanding, the function to derive the rank change would be a multiple of the sigmoid function, right? What is the maximum rank change? Edit: (this is not an edit :stuck_out_tongue: - I just realized this) obviously the maximum would be double the middle, or 48! That doesn’t match up with your numbers though. Hmm…

3 Likes

this is not a perfect sigmoid function. Glicko is complicated.

2 Likes